Vector operations in two dimensions

Vector operations in two dimensions

Lessons

How to do addition, subtraction, multiplication and division on vectors in two dimensions

How to describe the angles of two dimensional vectors

How to solve for the angle and magnitude of two dimensional vectors with trigonometry.

Notes:

When adding, subtracting, multiplying, and dividing vectors in two dimensions, the same rules are followed as in one dimensional problems:

When vectors are added, the vector diagram is drawn by tip-to-tail addition. To add A⃗\vec{A}A and B⃗\vec{B}B, draw the vector A⃗\vec{A}A, then starting at the tip of A⃗\vec{A}A draw B⃗\vec{B}B. The tail of B⃗\vec{B}B connects to the tip of A⃗\vec{A}A.

Taking the negative of a vector "flips" the vector to point in the opposite direction, while keeping the same magnitude.

Multiplying or dividing a vector by a positive scalar changes the magnitude of the vector, while keeping the same direction.

The graphical solution to a vector problem in two dimensions can make a vector triangle that can be solved using trigonometry.

In this course we will be using navigational notation to specify the angles of vectors, which also called to compass notation when compass directions are used in the problem. Some examples of this notation:

A student arrives at school and from the entrance walks 20 m north to go to English. After, they walk 30 m east to physics class. What is their overall displacement? Answer with a vector diagram and a vector equation that describes the displacements.